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arXiv:2302.06688 · Journal of High Energy Physics

Linear response of entanglement entropy to $$ T\overline{T} $$ in massive QFTs

Shachar Ashkenazi, Soumangsu Chakraborty, Zhanyu Ma, Tom Shachar

Published Apr 18, 2023• 5 citations
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Abstract

Abstract We compute the leading correction to entanglement entropy in $$ T\overline{T} $$ T T ¯ deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.

DOI
10.1007/jhep04(2023)077

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Linear response of entanglement entropy to TT‾ T\overline{T} TT in massive QFTs
Abstract We compute the leading correction to entanglement entropy in TT‾T\overline{T}TT T T ¯ deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.
In a ddd-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\mathrm{\ensuremath{\Delta}}=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $\mathrm{\ensuremath{\Delta}}=\frac{d+2}{2}$. There are two sources generating the logarithmic correction. One is the metric deformation and the other is the minimal surface deformation. In this work, we investigate the change of the entanglement entropy caused by the minimal surface deformation and find that the second order minimal surface deformation leads to an additional logarithmic correction.
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a relevant operator, providing a pertrubative expansion where the terms are correlation functions in the undeformed theory. The entanglement entropy for free massive fermions and scalars easily follows. Finally, we study entanglement entropy across a plane in a background geometry that is a deformation of flat space, finding new universal terms arising from mixing of geometry and couplings of the QFT.
The entanglement entropy correlates two quantum subsystems which are part of a larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in [Formula: see text] dimensions by applying numerical techniques to entanglement entropy approach. This (2+1)-dimensional massive theory can be obtained from the (3+1)-dimensional massless scalar field via dimensional reduction. We also calculated mass corrections to entanglement entropy for scalar field. Finally, we observe that the area law contribution to the entanglement entropy is not affected by this mass term and the universal quantities depend upon the basic properties of the system.
We compute entanglement entropy for free massive scalar fields in anti-de Sitter (AdS) space. The entangling surface is a minimal surface whose boundary is a sphere at the boundary of AdS. The entropy can be evaluated from the thermal free energy of the fields on a topological black hole by using the replica method. In odd-dimensional AdS, exact expressions of the Rényi entropy S n are obtained for arbitrary n. We also evaluate 1-loop corrections coming from the scalar fields to holographic entanglement entropy. Applying the results, we compute the leading difference of entanglement entropy between two holographic CFTs related by a renormalization group flow triggered by a double trace deformation. The difference is proportional to the shift of a central charge under the flow.
Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the coefficient of this term is independent of the state of the boundary theory. In fact, the same is true of all of the coefficients of contributions which diverge as some power of the UV cut-off. Secondly, we show that the relevant deformation introduces new logarithmic contributions to the entanglement entropy. The form of some of these new contributions is similar to that found in investigations of entanglement entropy in a free massive scalar field theory [1, 2].